Solvability of partial differential equations of nonlinear totally characteristic type with resonances

Abstract

Let us consider the following nonlinear singular partial differential equation (t∂/∂ t)^mu=F(t, x, {(t∂/∂ t)^j(∂/∂ x)^αu}_{j+α≤ m, j<m}) in the complex domain. When the equation is of totally characteristic type, the author has proved with H. Chen in [{2}] the existence of the unique holomorphic solution provided that the equation satisfies the Poincaré condition and that no resonances occur. In this paper, he will solve the same equation in the case where some resonances occur.